Lookback Option Pricing Problem In Uncertain Environment

With the development of the financial market,options,one of the most popular derivatives,play an increasingly important role in the financial field.Lookback option is a type of strong path-development option whose payoff depends on the maximum or minimum value of asset price reached during the life of the option which give investors the opportunity to obtain the best payoff.This paper discusses the problem of Lookback option pricing based on uncertain theory.The main results are as follows:(1)Valuation of the traditional option price theory is based on the framework of the probability theory.In the actual financial market,however,people's decision-making rely on nonlinear transformation of probability,so the belief degree exerts an impor-tant impact people's decision-making.Under the framework of uncertainty theory and the assumption of risk-free interest rate,using uncertain differential equation to de-scribe the change process of stock price,the Lookback option pricing was studied by introducing Liu's uncertain stock price model,mean-reverting model and exponential Ornstein-Uhlenbeck model.According to the property that option short position and long position have the same expected discount return,the Lookback call option and put option pricing formulas are obtained by using ?-path of uncertain differential e-quation and uncertainty analysis method.By comparing Liu's uncertain stock price model,mean-reverting model and exponential Ornstein-Uhlenbeck model,We think that exponential Ornstein-Uhlenbeck model is more practical in financial market.(2)Rate is one of the factors that affect the price of derivatives,and its fluctuation will have a significant impact on the whole economy.This paper considers the influence of interest rate on stock price.And then three improved uncertain interest rate stock price models are introduced on the basis of Liu's uncertain stock price model,mean-reverting model and exponential Ornstein-Uhlenbeck model.According to the property that option short position and long position have the same expected discount return,the more practical Lookback option pricing formulas are obtained by using uncertainty analysis method.